Re: Why dose a lake only freeze about a couple feet deep?

A. We must observe that if all the water in the lake would freeze there
could be no living superior organism (like a fish) in there.

B. The main reasons why only a thin cover neighbouring the contact
surface between water and air freezes are:
 - an odd property of water: it has a lower density at a temperature
   of 4 degrees Celsius than it has at 0 degrees Celsius.
 - the heat exchange between water and air is faster than the
   water-ice or water-earth heat exchange.

C. Now let's look in more detail at this two reasons.
 1. As you probably know, bodies tend to dilate (raise their volume)
    when heated. (E.g.: The railways of old trains or of the tram in
    San Fransisco are made of pieces with a little space left between
    them. This is why you hear that periodical noise when using one
    of thease. When the air has a temperature at 2 meters above earth
    surface of - let's say - 45 degrees C, the railways (metal parts 
    of ...) will reach 60 degrees C. Because of this the individual
    pieces tend to become longer and, sometimes, if the space left
    between them at normal temperature is insufficient then they might
    change their form so that a train will no longer advance in a
    rectilinear motion.)

    So now we know from experience that bodies tend to raise their
    volume if temperature raises. Of course, the mass of a dilating
    body remains constant because there is no change in the amount of
    substance it contains. This means we can say that a body which has
    a higher temerature tends to have a lower density (=mass/volume).

    Another thing to point at is that in a liquid bodies with lower
    desities will go upwards, while those with higher densities
    (compared to that of the liquid) tend to go downwards. If you
    want more information about this search for Archimedes law.
    (E.g.: A rock - which has a higher density compared to that of 
    water - will go down and settle at the bottom; a piece of wood
    - which has a lower density - will go up and settle at the surface,
    that is - it floats.)

    Now that we know all this we might assume that if we have water
    of two different temperatures in a tank then the one with a higher
    temperature (which means lower density) should stay on top of the
    other one. But this is true only for temperature greater than
    4 degrees C. At temperatures between 0 and 4 degrees C water has
    the peculiar property of having a greater density for greater
    tempertures. In other words, it dilates while _cooling_. This is
    why if we have water of two different temperatures - one 0 degrees C
    and the other 4 degrees C - the one which has a temperature of
    4 degrees will stay below the water with temperature 0 degrees C
    (before energy exchange as heat begins to have a considerable
    effect).

 2. Now let's see how the heat exchange takes place between water and
    air and then between water, ice and earth.

    When one wants to dry some laundry a good method is to hang them
    on a wire outside (if it is warm). After a time we observe that
    they cool and dry. This is due to evaporation (transformation of
    water from liquid into gas-vapours). But if you put outside a brick
    it will not cool, it will even get warm. 

    But why a does a substance cools when it evaporates? First we must
    explain what is temperature. We know that little tiny microscopic
    parts of objects (atoms / molecules) are always moving. We call
    this a thermic movement. (the macroscopic effect of this is the
    brownian motion) If this little parts move generaly faster than
    others in another body we say that the first body has a higher
    temperature than the other one.

    At the contact surface between water and air something interesting
    happens. Some of the faster molecules in the liquid escape. If we
    have less faster molecules we can say that the ones which remains
    move generaly slower so they have a _lower_ _temperature_.

    Another thing: The heat exchage is faster if the difference in
    temperature between the bodies is higher. But below ice (in our
    lake) is water with temperature 0 (and below this it gradualy
    reaches 4 degrees). So ice acts as an heat insulator.

    The flow of heat to the earth is somehow higher than the one to the
    ice but it is still small.